Suppose that y varies inversely with the square of x, and y=50 when x=4. Find y when x=5
The statement " y varies inversely as x means that when x increases, y decreases by the same factor. In other words, the expression xy is constant:
xy=k
where k is the constant of variation.
Here, it is given that yvaries inversely with the square of x and y=50 when x=4, therefore,
x2y=k⇒(4)2×50=k⇒k=16×2500⇒k=40000
Thus, the general equation is x2y=40000.
Since x=5, therefore,
x2y=40000⇒(5)2y=40000⇒25y=40000⇒y=4000025=1600
Hence, y=1600 when x=5.